Note that these words can be any number of syllables, but what makes them single morphemes is that they cannot be divided further into meaningful units. Mango, for example, has no internal meaning of man or go; it is a single morpheme that means, roughly, "a tropical ovoid fruit, which grows on a tree of the same name, is orange when ripe, etc." Additionally, though -er is a suffix used to mean "one who does" (and also as a comparative, for adjectives, meaning "more"), wat is not a morpheme, as it carries no meaning, so water is a single morpheme.

What makes these morphemes free is the fact that they may be used as stand-alone words. In constrast, bound morphemes cannot be used in this way and must be attached to a root (all morphemes are either free or bound). The following are the words above with bound morphemes added in bold:

mangoes

huckleberry

hottest

waterer

disestablish

(she) runs

Chomskyite

(Note that spelling sometimes changes when a morpheme is added, but spelling is meaningless for linguistic purposes.)
These morphemes do carry meaning (-s for example, tells us that there's more than one mango), but none of these morphemes can be used on their own. You cannot simply say er, or dis (without changing the meaning to the verb diss), which is how they differ from free morphemes.